AP Physics B1
Chapter 2- Motion in One Dimension
Questions for Discussion
Distance, Displacement, Velocity, Speed and Acceleration (Sec. 1 to 9)
1. Observer A measures the motion of an ant relative to a coordinate system bolted to the ground.
Observer B uses a coordinate system bolted to the floor of a moving bus. Which of the
following would be the same for both observers?
(a) displacement of the ant
(b) speed of the ant
(c) time it takes the ant to move
2. Can the distance an object travels be greater than zero when the object’s displacement is zero?
If so, give an example.
3. Does the displacement of an object in your reference frame depend on the location you chose
for the origin of your coordinate system?
4. Can distance traveled ever be less than the magnitude of the displacement? If so, give an
example.
5. You have your car’s odometer reading at the start and end of a trip, as well as the elapsed time
for the trip. Which of the following can you determine from these readings?
displacement, distance, average velocity, average speed
6. An object travels v meters per second for d meters and then 2v meters per second for d meters.
The average speed for the entire trip is (less than, equal to, greater than) 1.5 v meters per
second. Explain your reasoning.
7. A car travels 80 km/h for 3.0 h and then 40 km/h for 2.0 h.
(a) What is the average speed for the entire trip?
(b) If the car travels in the positive direction during the first part of the trip then the average
velocity for the trip is either ___ or ___.
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8. Can speed ever be negative?
9. Under what conditions will average speed equal the magnitude of the average velocity?
10. If a car reverses direction then must its instantaneous velocity equal zero at some instant?
11. If two objects have the same instantaneous speed may they have different instantaneous
velocities? If so, give an example.
12. If two objects have the same instantaneous velocity may they have different instantaneous
speeds? If so, give an example.
13. Give an example of an object that moves as described for each of the following.
(a) The acceleration is zero but the average velocity is not zero.
(b) The instantaneous velocity is zero but the acceleration is not zero.
(c) The acceleration is negative and the instantaneous velocity is positive.
(d) The acceleration is positive and the instantaneous velocity is negative.
(e) The object is speeding up and the acceleration is negative.
(f) The object is slowing down and the acceleration is positive.
(g) The acceleration is positive and the instantaneous velocity decreases with time.
14. A car is moving in reverse (the negative direction) when its accelerator gets stuck on the floor.
Give the sign of acceleration and the sign of instantaneous velocity for this car.
15. Give one example in which we can not treat a moving ball as a point mass- an object with no
internal structure.
Equations of Motion With Constant Acceleration, Freely Falling Bodies
16. An airplane lands with an initial velocity of 90.0 m/s. After 25.0 s, the plane is 1200 m from
the place it landed.
(a) Calculate the acceleration of the plane during the 25.0 s interval.
(b) Calculate the velocity of the plane after 25.0 s.
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17. A bullet leaves the barrel of a rifle with a speed of 500 m/s. The barrel of the rifle is .70 m
long.
(a) What is the bullet’s acceleration while it is in the rifle barrel?
(b) For how long is the bullet in the barrel?
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18. An object moving with constant velocity in the positive x direction passes the origin at t= 0.
The object’s velocity is 20 m/s. At t= 5.0 s, a force causes the object to accelerate uniformly
at –4.0 m /s2 .
(a) What is the object’s position at t= 12 s?
(b) What is the object’s velocity at t= 12 s?
€ is the object’s position x= 80 m?
(c) At what times
€ (d) At what time (t > 0) does the object return to the origin?
(e) How far does the object travel from t= 6.0 s to t= 7.0 s?
Hint:
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You need equations for position and velocity for 0≤ t≤ 5.0 s and another set of position and
velocity equations for t ≥ 5.0 s.
19. A boat is initially at rest. The boat sinks at a location where the ocean’s depth is 320 m. Due
to resistance of the seawater, the sinking boat reaches a terminal speed of 8.0 m/s after falling
for 20 s.
(a) What is the magnitude of the boat’s (constant) acceleration during the 20 s it is reaching
terminal speed?
(b) Assuming the acceleration was constant, at what depth below the surface did the boat reach
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terminal speed?
(c) How long after the boat begins to sink did it reach the bottom€of the ocean?
20. An object begins moving from rest with constant acceleration. It travels D meters in T seconds.
Its final speed is V meters per second.
1
(a) At time t= T the instantaneous speed of the object
2
V
is (less than, equal to, greater than) . Explain.
2
1
D
(b) At
€ time t= 2 T the position x of the object is (less than, equal to, greater than) 2 .
Explain.
€
V
(c) When the instantaneous velocity is
the position x of the object is (less than, equal to,
2
€
€
D
greater than)
. Explain.
2
€ the air is 15.0 s.
21. The total time a ball remains in
(a) With what speed was the ball thrown straight upward?
(b) What
€ is the ball’s maximum height?
22. A stone is dropped from a tower 110 m tall. The stone’s initial velocity is zero.
(a) With what speed does the stone strike the ground?
(b) How long does it take the stone to reach the ground?
23. An experimental aircraft is accelerating upward at 15 m /s2 . At t= 0 the altitude of the aircraft
is 10000 m and its upward velocity is 25 m/s. The test pilot jumps from the aircraft at t= 0 and
opens his parachute when his altitude is 2000 m. Neglect air resistance before the pilot’s
parachute opens.
(a) How long after the pilot jumps does he€open his parachute?
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(b) What is the pilot’s speed when the parachute opens?
(c) How far below the aircraft€is the pilot at t= 4.0 s?
(d) How far above the ground is the pilot at t= 24 s?
(e) What is the difference between the pilot’s maximum altitude and his altitude at t= 0?
Hint:
Find functions that give the pilot’s velocity as a function of time, the pilot’s altitude as a
function of time and the aircraft’s altitude as a function of time.
24. A rocket is initially at rest. The rocket accelerates upward from ground level at 7.5 m /s2
for 100 s. The engine is then shut off. What is the maximum height reached by the rocket?
25. A ball is thrown straight upward. State the sign of instantaneous velocity and acceleration at
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each instant. Take upward as positive.
(a) the ball is moving upward and is at half of its maximum height
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(b) the ball is at its maximum height
(c) the ball is moving downward
26. A ball is thrown straight upward. Upward is the positive direction. Describe how acceleration
varies from the instant the ball leaves your hand to just before the ball strikes the ground.
27. Ball A is released from rest by a person standing on a roof. Ball B is thrown downward by the
person. Which of the following are different for ball A and ball B? acceleration, speed with
which the ball strikes the ground, time it takes ball to reach the ground
Explain.
28. Ball A is thrown downward by a person standing on a roof. Ball B is thrown upward with the
same speed by the person. Which of the following are different for ball A and ball B? velocity
with which the ball strikes the ground, time it takes ball to reach the ground.
Explain.
29. Ball A is released from rest by a person standing on a roof. Ball B is released from rest by the
person two seconds later.
(a) While both balls are falling the difference in their speed (increases, decreases, remains the
same). Explain.
(b) While both balls are falling their separation (increases, decreases, remains the same).
Explain.
30. A ball travels d meters in the first t seconds after it is dropped from rest. How far does the ball
travel in the next t seconds?
31.
x= 16 d
x= 4 d
x= d
x= 9 d
x= 25 d
In a classic demonstration, bolts are tied to a string. The spacing of the bolts is as shown
above. The assembly is picked up by the right end and dropped vertically onto a metal pie pan.
Students can clearly hear the sound each bolt makes when it strikes the ground. The time
between each sound (increases, decreases, remains the same) as the string falls. Explain.
32. The amount of weight in the air decreases as the string of question 31 falls. Does the rate at
which the string accelerates downward change as a result? Explain.
33. Tom wants to fire his gun on the Fourth of July. To avoid hurting people, Tom plans to fire
his gun straight upward. Why is this not a good idea?
34. When a ball is thrown straight upward and air resistance is ignored, the speed of the ball when
it is h meters above the launch point moving upward is the same as when it is h meters above
the launch point moving downward. The time the ball takes to reach its maximum height is the
same as the time it takes the ball to fall to its original height from the maximum height. Air
resistance is a force that is always directed in the direction opposite the ball’s motion. If air
resistance is taken into account then the time the ball spends falling is (less than, equal to,
greater than) the time it spends rising. Include a convincing argument to support your answer.
Position vs. Time and Velocity vs. Time Graphs
35. Consider the following position vs. time graph.
20
15
10
position (m)
5
0
–5
–10
–15
–20
0
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
2
4
6
8
10 12
time (s)
14
16
18
20
At what times is the position zero meters?
What is the displacement of the object from t= 4 s to t= 16 s?
What is the total distance traveled from t= 4 s to t= 16 s?
What is the instantaneous velocity of the object at t= 9 s?
At what times is the instantaneous velocity of the object greatest?
At what times is the instantaneous speed of the object greatest?
At what times is the object at rest?
At what times (0< t< 20 s) is the instantaneous velocity not defined?
Sketch the velocity vs. time graph corresponding to the position vs. time graph.
What is the average velocity over the time interval t= 5 s to t= 15 s?
What is the average speed over the time interval t= 5 s to t= 15 s?
36. Answer each question by selecting A, B, C, D, E, F or none of these.
position
A
time
F
B
E
C
D
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
At which point is the object at rest?
At which point is the acceleration negative?
At which point is the acceleration positive?
At which point is the instantaneous speed greatest?
At which point is the object at the origin?
At which point is the instantaneous velocity undefined?
At which three points is the object moving to the right (right is the positive direction)?
At what point is the instantaneous velocity negative?
37. Answer the following questions based on the velocity vs. time graph.
+20
+16
€
+12
€
€
€
€
velocity (m/s)
+8
+4
0
−4
−8
€
−12
€
−16
€
0
€
2
4
6
8
10
12
14
16
18
20
time (s)
Note:
The graph is a horizontal line from t= 15 to t= 16 s.
The graph is curved from t= 16 s to t= 20 s.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
At what times is the object at rest?
At what times is the object’s acceleration zero?
What is the object’s acceleration at t= 2 s?
What is the object’s acceleration at t= 12 s?
At what two times is the object’s acceleration undefined (0 < t < 20 s)?
At what times is the acceleration defined and increasing?
Suppose you wanted to calculate the time at which the object returns to the position it had
at t= 0. Do not calculate the time, but state the geometric condition that the graph would
satisfy when the object returns to its original position.
How far does the object travel from t= 2 s to t= 4 s?
What is the object’s average velocity from t= 0 to t= 6 s?
For what values of time is the object’s speed decreasing?
At what times is the object’s position most negative?
38. Answer the following questions based on the velocity vs. time graph.
B
velocity
A H
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
G
C
F
D
time
E
At what three times is the object’s instantaneous speed increasing?
At what two times is the object’s instantaneous speed decreasing?
At what time is the object’s acceleration undefined?
At what time is the object’s instantaneous velocity constant?
At what time is the object’s acceleration defined and decreasing?
At what time is the object at rest?
At what two times is the acceleration of the object defined and largest in magnitude?
At what time is the object’s acceleration positive and its instantaneous speed decreasing?
39. Match each description with one of the graphs shown below. Each graph can be used as many
times as necessary. Write D if no graph matches a description.
A
B
C
t
1.
2.
3.
4.
5.
6.
7.
8.
t
t
Velocity vs. time graph for an object whose acceleration is increasing.
Velocity vs. time graph for an object that is not moving.
Velocity vs. time graph for an object whose acceleration is zero.
Velocity vs. time graph for uniform positive acceleration.
Acceleration vs. time graph for constant instantaneous velocity.
Position vs. time graph for uniform positive acceleration.
Position vs. time graph for positive constant instantaneous velocity.
Position vs. time graph for an object that is not moving.
40.
x
x
x
t
v>0
velocity decreases
with time
t
v<0
velocity decreases
with time
x
t
v>0
velocity increases
with time
t
v<0
velocity increases
with time
The four position vs. time graphs shown above illustrate how the shape of the graph varies with
the sign of velocity and acceleration. A curve like the one in the graph on the left is said to be
concave downward. It has a shape like an inverted bowl. A curve like the one in the graph on
the right is said to be concave upward. It has a shape like a right side up bowl. Generalize
these examples to come up with a rule that relates the shape of a position vs time graph and the
sign of the acceleration.
41.
v
t
Describe in words how the speed of the object whose velocity vs time graph is shown varies
with time.
42. Sketch a velocity vs. time graph for an object whose velocity increases with time and whose
acceleration decreases with time.
43. A ball is thrown straight upwards. Sketch a position vs time graph, velocity vs. time graph and
acceleration vs. time graph for the motion of the ball.
44. A superball is dropped from rest and rebounds to the height from which it was dropped.
Sketch a position vs. time graph and velocity vs time graph for the motion of the ball from the
time it is released to just before the third bounce. Place the velocity vs. time graph directly
below the position vs. time graph and use the same time scale so that the position vs. time
representation can be compared directly to the velocity vs. time representation.
45. Consider an acceleration vs time graph.
(a) Does the slope of the graph equal any of the quantities we have used to describe motion
in this chapter? If not then what would the slope mean?
Δv
(b) According to the equation a =
, what does the area under an acceleration vs time graph
Δt
from t I to t F equal?
average acceleration from t I to t F , average velocity from t I to t F , or change in
instantaneous velocity from t I to t F
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46. €Weathermen
collect rain water in a cylinder called a rain gauge to determine the amount of rain
that falls. Suppose you
graph of the depth€of water
€ produce
€
€ in the rain gauge as a function of
time. What characteristic
of
the
graph
is
related
to
how
hard the rain falls?
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